For the Appell function with one of the arguments equal to 1 we have [1]}
\(F_1\left(\begin{array}{l}a,b_1,b_2 \\c\end{array};x,1\right)=\dfrac{\Gamma (c)\Gamma (c-a-b_2)}{\Gamma (c-a)\Gamma (c-b_2)}\,\mbox{}_{3}F_{2}\!\left(\genfrac{}{}{0.0pt}{}{a,b_1,a+1-c}{c,a+b_2-c+1};x\right)\) 
